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Plane TrigonometryTrigonometrical Ratios606 Let 𝑂𝐴 be fixed, and let the revolving line 𝑂𝑃 describe a circle round 𝑂. Draw 𝑃𝑁 always perpendicular to 𝐴𝐴'. Then, in all positions of 𝑂𝑃.𝑃𝑁𝑂𝑃= the sine of the angle 𝐴𝑂𝑃. 𝑂𝑁𝑂𝑃= the cosine of the angle 𝐴𝑂𝑃. 𝑃𝑁𝑂𝑁= the tangent of the angle 𝐴𝑂𝑃. 607 𝑃𝑁 always perpendicular to 𝐴𝐴'. Then, in all positions of 𝑂𝑃. If 𝑃 be above the line 𝐴𝐴', If 𝑃 be below the line 𝐴𝐴', If 𝑃 lies to the left of BB', Relations between the trigonometrical functions of the same angle.613606 617 If 𝑎𝑏, 𝑎 𝑏606 618 ; 11+617 619 The Complement of 𝐴 is = 90°−𝐴 620 The Supplement of 𝐴 is = 180°−𝐴 621 ExampleTo find all the ratios of 660°. Measuring 300° (=660°−360°) round the circle from 𝐴 to 𝑃, we find the acute angle 𝐴𝑂𝑃 to be 60° and 𝑃 lies below 𝐴𝐴′, and to the right of 𝐵𝐵′.Therefore √32 12and from the sine and cosine all the remaining ratios may be found by (610-616). 626 Inverse NotationThe angle whose sine is 𝑥 is denoted byAll the angles which have a given sine, cosine, or tangent, are given by the formula, These formula are verified by taking 𝐴, in Fig. 622, for 𝜃, and making 𝑛 an odd or even integer successively. Sources and Referenceshttps://archive.org/details/synopsis-of-elementary-results-in-pure-and-applied-mathematics-pdfdrive©sideway ID: 210800027 Last Updated: 8/27/2021 Revision: 0 Ref: References
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